Approximating Concavely Parameterized Optimization Problems
2012-12-01NeurIPS 2012Unverified0· sign in to hype
Joachim Giesen, Jens Mueller, Soeren Laue, Sascha Swiercy
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ReproduceAbstract
We consider an abstract class of optimization problems that are parameterized concavely in a single parameter, and show that the solution path along the parameter can always be approximated with accuracy >0 by a set of size O(1/). A lower bound of size (1/) shows that the upper bound is tight up to a constant factor. We also devise an algorithm that calls a step-size oracle and computes an approximate path of size O(1/). Finally, we provide an implementation of the oracle for soft-margin support vector machines, and a parameterized semi-definite program for matrix completion.